Civil Engineering 2021 Paper II 50 marks Compulsory Calculate

Q5

(a) A one-hour unit hydrograph of a catchment is shown in the figure. A storm of two hours duration with intensity of 70 mm/h in the first hour and 40 mm/h in the second hour occurs over the catchment. Calculate the peak direct surface runoff value in m³/s. (10 marks) (b) A temporary coffer dam is to be built to protect the 5 year construction activity for a major river valley project. If the coffer dam is designed to withstand the 25-year flood, what is the risk that the structure will be overtopped in the third year? (10 marks) (c) A weir across an alluvial river has a horizontal floor length of 50 m and retains 5 m of water under full flow condition. The downstream sheet pile is driven to a depth of 5 m below the impervious floor of negligible thickness. Determine the exit gradient. (10 marks) (d) What is an indicator organism ? Discuss the required characteristics for an ideal indicator organism. Name any two indicator organisms. (10 marks) (e) Circular sewer of minimum diameter of 150 mm is recommended for the house connections. Calculate the discharge carried by this sewer, when flowing full, laid at a slope of 0·004. Take Manning's n as 0·013. Why this sewer size has been recommended as the minimum size, when the waste water discharge from individual household will be substantially less ? (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक जलग्रहण क्षेत्र का एक-घंटा एकांकी जलालेख चित्र में दर्शाया गया है । जलग्रहण क्षेत्र पर दो घंटे की अवधि की एक वृष्टि, 70 mm प्रति घंटा की तीव्रता के साथ पहले घंटे में एवं 40 mm प्रति घंटा की तीव्रता के साथ दूसरे घंटे में होती है । चरम प्रत्यक्ष धरातलीय अपवाह के मान की गणना m³/s में कीजिए । (10 अंक) (b) एक मुख्य नदी घाटी परियोजना की 5 वर्ष की निर्माण गतिविधि की सुरक्षा के लिए एक अस्थायी कॉफर बांध बनाया जाना है । यदि कॉफर बांध का अभिकल्पन 25-साल की बाढ़ को सहने के लिए किया गया है, तो इस संरचना के तीसरे साल में उत्लावन होने का जोखिम कितना है ? (10 अंक) (c) एक जलोढ़ नदी के आरपार स्थित एक विवर का क्षैतिज फर्श 50 m लंबा है एवं पूर्ण प्रवाह की स्थिति में 5 m पानी रोकता है । अनुप्रवाह (डाउनस्ट्रीम) शीट पाइल, अगम्य मोटाई के अपारगम्य फर्श के नीचे, 5 m गहराई तक डाली गयी है । निर्गम प्रवणता निर्धारित कीजिए । (10 अंक) (d) एक सूचक जीव क्या है ? एक आदर्श सूचक जीव के लिए आवश्यक अभिलक्षणों की विवेचना कीजिए । किन्हीं दो सूचक जीवों के नाम लिखिए । (10 अंक) (e) घरेलू संयोजन के लिए न्यूनतम 150 mm व्यास का वृत्ताकार मलक नल (सीवर) अनुशंसित है । इस मलक नल द्वारा प्रवाहित निस्सरण की गणना कीजिए, जब यह पूरा भरा बह रहा है एवं 0·004 के ढाल पर बिछाया गया है । मैनिंग के n को 0·013 लीजिए । इस मलक नल के आमाप की अनुशंसा न्यूनतम आमाप के रूप में क्यों की गयी है, जबकि पृथक घर से निस्सरित अपशिष्ट जल प्रवाह अत्यंत ही कम होगा ? (10 अंक)

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Directive word: Calculate

This question asks you to calculate. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Begin with the directive 'calculate' for the numerical parts (a), (b), (c), and (e), while 'discuss' applies to part (d). Allocate approximately 20% time to each sub-part given equal 10-mark weighting. Structure as: direct calculations for (a), (b), (c), (e) with clear steps, followed by a descriptive response for (d) on indicator organisms. No conclusion needed; present each part separately with clear labeling.

Key points expected

  • Part (a): Apply superposition principle to 1-hour unit hydrograph; convolute with 70 mm and 40 mm rainfall excesses lagged by 1 hour; identify peak DSR ordinate in m³/s
  • Part (b): Apply risk formula R = 1 - (1-1/T)^n where T=25 years, n=3 years; calculate exact probability of overtopping in third year specifically, not cumulative
  • Part (c): Use Khosla's theory for exit gradient; apply G_E = (H/d) × (1/π√λ) where λ = (1+√(1+α²))/2 and α = b/d; substitute b=50m, d=5m, H=5m
  • Part (d): Define indicator organism; list 4-5 ideal characteristics (e.g., consistently present in feces, non-pathogenic, easy to detect); name E. coli and Streptococcus faecalis or Coliform bacteria
  • Part (e): Apply Manning's equation Q = (1/n) × A × R^(2/3) × S^(1/2) for full circular pipe; explain 150 mm minimum prevents clogging by solids and maintains self-cleansing velocity

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies UH superposition principle for (a), risk probability concept for (b), Khosla's exit gradient theory for (c), indicator organism definition and characteristics for (d), and Manning's equation with self-cleansing velocity concept for (e)Identifies most concepts correctly but confuses risk formula application in (b) or misapplies Khosla's parameters in (c); partial understanding of indicator organism criteriaFundamental conceptual errors such as treating UH as direct runoff hydrograph without convolution, using wrong risk formula, applying Bligh's instead of Khosla's theory, or missing self-cleansing velocity concept entirely
Numerical accuracy20%10All five calculations yield precise values: correct peak DSR from UH convolution (a), exact risk probability ~11.5% (b), exit gradient ~0.14-0.15 (c), discharge ~0.015-0.016 m³/s (e); proper unit conversions throughoutCorrect methodology but arithmetic errors in 1-2 parts; minor unit conversion mistakes (mm to m, hours to seconds); approximately correct final valuesMajor calculation errors in multiple parts; wrong formulas leading to order-of-magnitude errors; missing units or inconsistent unit usage; incomplete calculations
Diagram quality15%7.5Clear sketch of UH with storm hydrograph superposition for (a); labeled coffer dam cross-section for (b); Khosla's flow net with key dimensions for (c); sewer cross-section with hydraulic elements for (e)Basic diagrams present but lacking labels or proper proportions; missing one required diagram; hand-drawn quality acceptable but unclearNo diagrams despite visual components needed; or completely misleading sketches that contradict the problem statement; illegible drawings
Step-by-step derivation25%12.5Systematic presentation: UH ordinates table with convolution steps for (a); explicit risk formula derivation with substitution for (b); complete Khosla's parameter calculation (α, λ, φ) for (c); Manning's equation expansion with hydraulic radius derivation for (e)Steps shown but condensed or missing intermediate substitutions; jumps from formula to answer without showing working; some logical gaps in derivation flowFinal answers only with no working; or completely wrong steps that don't lead to the stated answer; missing essential derivation components like φ value calculation in (c)
Practical interpretation20%10Interprets peak DSR significance for flood design; explains risk tolerance for temporary structures; relates exit gradient to piping failure and Khosla's safe value; connects indicator organisms to BIS drinking water standards; justifies 150 mm sewer with Indian plumbing code context and solid waste managementBrief mention of practical relevance without elaboration; generic statements about safety; partial connection to Indian standards or field conditionsPurely mathematical treatment with no physical interpretation; no mention of why results matter for engineering design or public health; ignores Indian context entirely

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